Conversation

Is there an easy algorithm to a) count the number of equivalent shortest paths on a manhattan grid b) enumerate them systematically? I wrote a dumb random algo and I could run it for a long time to count unique paths but I imagine there's a closed-form solution?
Image
7
9
Replying to
an easy way to enumerate them would be depth-first traversal of a binary decision tree, where you only take up to N x-moves and up to M y-moves, and bottom out when you've taken all of both
2